I shall present a review of my recent work on theoretical and computational modeling of the interactions of graphene with external charged particles in different contexts. Several comparisons with experiments will also be discussed.

In the first part, I shall present a stochastic model for fluctuations in the electrostatic potential induced in graphene by a random distribution of stationary charged impurities in the underlying substrate, when the other surface of graphene is exposed to air or to an electrolyte containing mobile ions. Next, I shall present results of a preliminary modeling of the differential capacitance of electrolytically gated graphene for sensing applications, where the effects of finite size of ions in an aqueous solution are studied in combination with the effects of the dielectric saturation and dielectric decrement in the solvent.

In the second part, I shall review several results on modeling the interaction of graphene with external charged particles that move in a broad range of energies, with a particular emphasis paid on the role of the collective electronic excitations in graphene. For slow charges moving parallel to graphene, a wake effect is predicted in the induced potential in graphene due to hybridization of the sheet (or Dirac) plasmon in graphene with the optical phonon modes in the underlying substrate. Interactions with fast charged particles are studied in the context of the Electron Energy Loss Spectroscopy of graphene, both in the reflection and transmission regimes. In particular, by adopting relativistic treatment for a fast charged particle traversing graphene, predictions are made for the emission of electromagnetic radiation in the far field regions in the form of transition radiation from single- and multi-layer graphene targets.

Possible applications are discussed for graphene-based nano-photonic devices in the terahertz to infrared range of frequencies.